# Theoretical value of a simple pendulum in motion

• S00_SUNNiE
In summary, the homework statement asks for the relationship between the length of a simple pendulum and the frequency of the pendulum. The student is asked to find the theoretical value for the length and frequency of a simple pendulum, as well as determine the error that may have been introduced in measuring the string and timing.
S00_SUNNiE

## Homework Statement

I'm new to this forum and I'm not very sure with how I'm suppose to state my problems, thus if it's written wrong please tell me so.

I'm currently doing a motion lab report for my physics class and we have to analyse the motion of a pendulum.
The material used for the lab are: Aparatus, string, 100g bob, and stopwatch (to measure time it takes to complete 30 cycles).
I'm asked to find the relationship between the length and the frequency of the simple pendulum.
i have finhsed mostly everything that's asked for in the lab but for the conclusion I'm asked to add the percent error, but my problem is what is a theoretical value?

## Homework Equations

This is the percent Error Formula:
(|theoretical value - experimental value|/theoretical vaule) x 100%

I've asked my teacher what is a theoretical value but she told me to look it up.

## The Attempt at a Solution

i've tried googling for the theoretical value and one site has stated that the theoretical value is 9.80m/s2. It too is a lab report about the motion of a simple pendulum but I'm not quite sure if the value is correct.

I am thinking that you graphed your data, something like Period vs squareRoot(L), to get a straight line. The accepted formula is T = 2(pi)*squareRoot(L/g) so on that graph theory predicts a slope of 2(pi)/squareRoot(g).
The % error would then be the % difference between your slope and the slope theory predicts.

Personally, I never liked that approach. The scientist usually doesn't know the "correct" value and must estimate the accuracy of measurement. Hey, maybe you can earn a bonus mark! What you do is run your data through a calculator and get the variation or deviation of the data from the line of best fit. (Calculators usually show it when you use the line of best fit feature.) Then you say, "the slope is ___ plus or minus ___".
Then you could say "this is (or isn't) equal to the accepted value to within the experimental error."

## 1. What is the theoretical value of a simple pendulum in motion?

The theoretical value of a simple pendulum in motion is the time period it takes for the pendulum to complete one full swing. This value is based on the length of the pendulum and the acceleration due to gravity.

## 2. How is the theoretical value of a simple pendulum in motion calculated?

The theoretical value of a simple pendulum in motion can be calculated using the equation: T = 2π√(L/g), where T is the time period, L is the length of the pendulum, and g is the acceleration due to gravity.

## 3. How does the length of a pendulum affect its theoretical value in motion?

The length of a pendulum has a direct effect on its theoretical value in motion. A longer pendulum will have a longer time period, while a shorter pendulum will have a shorter time period. This is because the longer pendulum has a larger arc to travel and thus takes longer to complete one swing.

## 4. What is the significance of the theoretical value of a simple pendulum in motion?

The theoretical value of a simple pendulum in motion is important in understanding the principles of pendulum motion and its relationship with gravity. It is also used in various scientific experiments and calculations involving pendulums.

## 5. How does the theoretical value of a simple pendulum in motion compare to its real-life value?

The theoretical value of a simple pendulum in motion is an ideal value, assuming perfect conditions and no external factors. In reality, factors such as air resistance and friction will affect the motion of a pendulum, resulting in a slightly different, but still close, real-life value.

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